Read about operation on sets as taught in schools
A and B are two sets.
 Complementation
Complement of sets A and B is denoted as A\B. A\B has the elements of A excluding the common elements of B. The complement of set A is denoted as A^{c}. A\B = {x : x∈A and x∉B}
 Intersection
Intersection of sets A and B is the set of all elements that belong to both the sets. It is represented as A∩B. A∩B = {x : x∈A and x∈B}
 A∩B⊆A
 A∩B⊆B
 A⊆B ⇒ A∩B = A
 A∩A = A
 A∩φ = φ
 A∩B = B∩A
 A\B = A∩B^{c}
 Union
Union of sets A and B is the set of all elements that belong to any the sets. It is represented as A∪B. A∪B = {x : x∈A or x∈B}
 A∪A⊆A
 A∪B = B∪A
 A∪φ = A
 If A⊆C and B⊆C = (A∪B)⊆C
 Distributive Laws:
 A∩(B∪C) = (A∩B)∪(A∩C)
 A∪(B∩C) = (A∪B)∩(A∪C)
 De Morgan's Laws:
 (B∪C)^{c} = B^{c}∩C^{c}
 (B∩C)^{c} = B^{c}∪C^{c}
